Bernd{Holger Schlinglo Institut f ur Informatik, Technische Universitat M unchen, e-mail: [email protected] Wolfgang Heinle Institut f ur angewandte Mathematik, Universitat Bern, e-mail: [email protected] Abstract In this work we survey the connections between modal logic and relation algebra. We compare various modal and relational languages for the speci cation of reac...

Rough set theory is proposed as the theoretical foundation of information systems and has found rapidly growing applications in intelligent data analysis. An especially interesting problem is its relationship with other knowledge representation formalisms. The most well-known result is that it can provide a semantics for modal logics. Motivated by the strong analogy between quantiiers and modal...

Forthcoming in the Journal of Aritificial Intelligence We introduce mathematical programming and atomic decomposition as the basic modal (T-Box) inference techniques for a large class of modal and description logics. The class of description logics suitable for the proposed methods is strong on the arithmetical side. In particular there may be complex arithmetical conditions on sets of accessib...

The modal μ-calculus is an extension of modal logic with two operators μ and ν, which give the least and greatest fixpoints of monotone operators on powersets. This powerful logic is widely used in computer science, in the area of verification of correctness of concurrent systems. In this survey we review both the theoretical aspects of the modal μ-calculus and its applications to computer scie...

Evaluating complex propositions requires evaluating truthvalues and assigning modal operators. Previous research suggested that evaluating truth-values may be the key to assigning modal operators. This study placed 111 third and fifth grade children in one of three training conditions: no training, training truth-value assignment, and training truthvalue and modal operator assignment. The resul...

Modal Kleene algebras are Kleene algebras with forward and backward modal operators, defined via domain and codomain operations. They provide a concise and convenient algebraic framework that subsumes various popular calculi and allows treating quite a number of areas. We survey the basic theory and some prominent applications. These include, on the system semantics side, wlp and wp calculus, P...

In this paper we present a tableau-like proof system for multi-modal logics based on D’Agostino and Mondadori’s classical refutation system KE [DM94]. The proposed system, that we call KEM , works for the logics S5A and S5P(n) which have been devised by Mayer and van der Hoek [MvH92] for formalizing the notions of actuality and preference. We shall also show howKEM works with the normal modal l...

This paper formalizes the communication of agents with modal operators in arrow logic. A communication between agents consists of an agent's utterance and the other agent's perception, thus, both of the utterance and the perception are regarded as parts of a communication channel between agents. Information is regarded as a propositional content of a sentence. An information channel where infor...

Symbolic transition systems separate data from process behaviour by allowing the data to be uninstantiated Designing a HML like modal logic for these transition systems is interesting because of the subtle interplay between the quanti ers for the data and the modal operators quanti ers on transitions This paper presents the syntax and semantics of such a logic and discusses the design issues in...

Symbolic transition systems separate data from process behaviour by allowing the data to be symbolic. Designing a HML-like modal logic for these transition systems is interesting because of the subtle interplay between the quantiiers for the data and the modal operators (quantiiers on transitions). In this paper a logic is deened, with a denotational semantics. The logic has been designed so as...